Optimal quadrature formulas for approximate solution of the first kind singular integral equation of with Cauchy kernel

Dilshod M. Akhmedov, Kholmatvay M. Shadimetov

Abstract


In the present paper in $L_2^{(m)}(-1,1)$ space the optimal
quadrature formulas with derivatives are constructed for
approximate solution of a singular integral equation of the first kind with Cauchy kernel. Approximate solution is obtained applying optimal quadrature formulas (OQF). Explicit forms for the of OQF`s are obtained. Some numerical results are presented.


Keywords


optimal quadrature formulas; the extremal function; Sobolev space; optimal coefficients; Cauchy type singular integral; weight function; singular integral equation

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DOI: http://dx.doi.org/10.24193/subbmath.2022.3.15

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